This invention relates generally to a receiving system. More specifically, the present invention relates to a signal processor in a receiver system for real-time wavelet de-noising applications.
Communications systems, radar systems, sonar systems and the like have a receiver which is used to detect the presence of specific signals and a signal processor to extract the information being transmitted within the signal. A problem with many of these types of systems is the detection of the received signal in the presence of noise and clutter and extracting information from the detected received signal with minimal loss due to noise and clutter.
Current systems have employed de-noising methods in the signal processor of the receiver. In particular, current systems are utilizing wavelet techniques for de-noising received signals. De-noising exploits important characteristics of wavelets, including multi-resolution capabilities and perfect reconstruction. Wavelet theory involves representing general functions in terms of simpler fixed building blocks at different scales and positions in time.
The main goal of wavelet transforms is to decompose the information contained in a signal into characteristics of different scales. This can be thought of as a means to describe the input waveform over a unit of time at different resolutions in time and frequency or scale. This signal decomposition technique is performed with the Discrete Wavelet Transform. A principle advantage of decomposing the input signal over a multi-scale wavelet representation is that the desired signal has the degree of freedom to be designed to correlate with the transforming wavelet function, thus having the property of non-signal like features to not correlate as well with the transformation function. Thus, when the signal is seen in the wavelet domain, its representation is apparent by large coefficients while the undesired signal will be represented by much smaller coefficients and will also typically be equally distributed across all the wavelet decomposition scales. Therefore, when a wavelet transformation output is put through a threshold function by some rule such as the soft, hard, or gradient threshold rule, the noise-like coefficients can be removed from the wavelet coefficient sets across all scales. When the altered wavelet coefficients have been re-transformed back to the time domain via an Inverse Wavelet Transformation, the coefficients corresponding to the desired signal will remain with the noisy coefficients removed or de-emphasized and the reconstructed waveform can be considered de-noised and thus of a higher quality.
Current wavelet de-noising algorithms pick a wavelet decompositions scale-specific de-noising threshold based on the received signal""s statistics. Some of the statistics used to calculate t are the number of input samples [N], noise standard deviation ["sgr"], and correlation factors ["sgr"j,xcex4L,xcfx86,KN] as shown in equations 1 and 2 below.
t="sgr"{square root over (2 log N)}xe2x80x83xe2x80x83Equation 1
Equation 1 can be extended for wavelet decompositions that are not orthogonal, and thus produce correlated DWT coefficients, by the inclusion of a cross-correlation factor in the threshold equation. This is shown below where xcex4L,xcfx86 is the jth scale""s cross-correlation of the non-orthogonal wavelet coefficients and KN is the scale dependent data set""s size.
tN,xcfx86,L(J)="sgr"j{square root over (2(1+xcex4L,xcfx86) log (KN))}xe2x80x83xe2x80x83Equation 2
The more unbiased the statistics are, the more optimal and reliable the de-noising performance the thresholding solution will provide. The reliability of the statistics is therefore limited by the quality and size of the data set from which the statistics are derived. Reliable and unbiased statistical requirements naturally lead to larger and larger data sets and thus larger and larger memory. Sophisticated data handling issues therefore must be applied to store and manage said data sets.
A further complication in current systems is the decision to use global vs. local statistics. These data set boundaries from which the statistics are derived thus imply being either on a small packet scale, such as a single burst of communications from a single subscriber, or on a system level multi-packet scale, such as conglomerate statistics of subscriber serving groups or time variant single subscriber communications as are seen in a multi-carrier cable or wireless communications systems. These statistical requirements do not apply reliably or gracefully for latency sensitive applications, as latency is inherently ignored. One of the reasons that latency is ignored is the algorithm requires a-priori knowledge of the full data set""s statistics prior to setting the de-noising threshold values and thus additional steps of data analysis and buffering prior to the wavelet thresholding stage must be performed. This is due to the desire to optimize the de-noising threshold. Again, the difficulty of choosing local vs. global statistics is a de-noising performance reliability variable. This further strains the memory and data handling issues and real-time requirements suffer further. Therefore the need for sufficient signal data to derive unbiased statistics exacerbates latency vs. performance issues and in real-time communications requires prohibitively long processing times.
The interpretation of the local and global statistics can also be misleading. In the case of local statistics, such as bursts communication between a subscriber and its infrastructure, the reliability of its statistical properties have a high probability of being skewed from its true characteristics due to insufficient data size. This will lead to a poor choice for the wavelet de-noising threshold value that either does not improve performance for the computational effort or mistakenly distorts the signal severely by over estimating the threshold values and acceptable/marginal performance is degraded/destroyed.
On the other hand global statistics, such as the conglomerate of many burst communications between single or multiple subscribers and its infrastructure, can be misleading. The communications medium cannot in many cases be assumed to have the same physical path characteristics for each subscriber in a serving group and/or may exhibit time invariant signaling performance for the single/multiple subscribers. From these perspectives local and global statistics are considered less than optimal and potentially very unreliable for real-time signal processing applications.
Accordingly, there exists a need for a signal processing approach/technique/algorithm to utilize wavelet de-noising techniques without the restrictions of the statistical, gradient searching, or memory and data handling issues of the current signal processing approaches/techniques/algorithms.
The present invention is a method and system for extracting information from a received signal with minimal loss due to noise. The system is comprised of a transformer, for correlating the received signal to a wavelet function and producing wavelet decomposition coefficients, a threshold circuit, which is responsive to the received signal, for applying predetermined threshold values based on the type of signal. Also included in the system is a filter, coupled to the transformer and threshold circuit, for altering the wavelet decomposition coefficients produced by the transformer using threshold values applied by the threshold circuit to produce altered wavelet coefficients from which the received signal is reconstructed with reduced noise.